数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 909-924.doi: 10.1016/S0252-9602(11)60285-3

• 论文 • 上一篇    下一篇

MULTIPLE SOLUTIONS FOR ASYMPTOTICALLY LINEAR ELLIPTIC EQUATIONS INVOLVING NATURAL GROWTH TERM

张贻民|沈尧天   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, |Wuhan 430071, China; Department of Mathematics, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2009-07-13 修回日期:2010-03-03 出版日期:2011-05-20 发布日期:2011-05-20
  • 基金资助:

    Project supported by the National Science Foundation of China (10771074;  10801055) and  Doctoral Program of NEM of China (200805611026).

MULTIPLE SOLUTIONS FOR ASYMPTOTICALLY LINEAR ELLIPTIC EQUATIONS INVOLVING NATURAL GROWTH TERM

 ZHANG Yi-Min, SHEN Yao-Tian   

  • Received:2009-07-13 Revised:2010-03-03 Online:2011-05-20 Published:2011-05-20
  • Supported by:

    Project supported by the National Science Foundation of China (10771074;  10801055) and  Doctoral Program of NEM of China (200805611026).

摘要:

In this article, under some conditions on the behaviors of the perturbed function f(x, s) or its primitive F(x, s)=∫0s f(x, t)dt near infinity and near zero, a class of asymptotically linear elliptic equations involving natural growth term is studied. By computing the critical group, the existence of three nontrivial solutions is proved.

关键词: critical group, weak slope, singular homology group, non-smooth Morse theory

Abstract:

In this article, under some conditions on the behaviors of the perturbed function f(x, s) or its primitive F(x, s)=∫0s f(x, t)dt near infinity and near zero, a class of asymptotically linear elliptic equations involving natural growth term is studied. By computing the critical group, the existence of three nontrivial solutions is proved.

Key words: critical group, weak slope, singular homology group, non-smooth Morse theory

中图分类号: 

  • 35J20